A hybrid of the optimal velocity and the slow-to-start models and its ultradiscretization

Details A hybrid of the optimal velocity and the slow-to-start models and its ultradiscretization A hybrid of the optimal velocity and the slow-to-start models and its ultradiscretization

2009-08-24

arxiv.org/abs/0908.3377v2

Nonlinear Sciences

Cellular Automata and Lattice Gases

11 pages, 3 figures, corrected typos, accepted for publication in JSIAM Letters

Scientific paper

Through an extension of the ultradiscretization for the optimal velocity (OV) model, we introduce an ultradiscretizable traffic flow model, which is a hybrid of the OV and the slow-to-start (s2s) models. Its ultradiscrete limit gives a generalization of a special case of the ultradiscrete OV (uOV) model recently proposed by Takahashi and Matsukidaira. A phase transition from free to jam phases as well as the existence of multiple metastable states are observed in numerically obtained fundamental diagrams for cellular automata (CA), which are special cases of the ultradiscrete limit of the hybrid model.

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